Non-affine horocycle orbit closures on strata of translation surfaces: new examples

We investigate specific examples of locally-defined real vector-fields on strata of translation surfaces. Integrating SL(2,R)-loci of Veech surfaces along these vector-fields yield interesting new examples of horocyle-invariant ergodic measures. These measures are supported on closed immersed manifolds with boundary that approach the boundary of strata in a novel way.Comment: 48 pages, 27 figures. Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosoph

The Inflaton Portal to Dark Matter

We consider the possibility that the inflaton is part of the dark sector and interacts with the standard model through a portal interaction with a heavy complex scalar field in equilibrium with the standard model at high energies. The inflaton and dark matter are encapsulated in a single complex field and both scalar sectors are charged under different (approximate) global U(1)'s such that the dark matter, as well as the visible pseudo-scalar are taken to be relatively light, as pseudo Nambu-Goldstone bosons of the theory. The dark matter relic density is populated by Freeze-In productions through the inflaton portal. In particular, after the reheating, production of dark matter by inflaton decay is naturally suppressed thanks to Planck stringent constraints on the dark quartic coupling, therefore preserving the non thermal scenario from any initial condition tuning.Comment: 11 pages, 5 figures, citations added, typos corrected, comments adde